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Isomorphic Group Rings Over Domains

Published online by Cambridge University Press:  20 November 2018

Isabelle Adjaero  and
Eugene Spiegel
Isabelle Adjaero
Affiliation:
University of Nigeria-Nsukka, Ahambra State, Nigeria
Eugene Spiegel
Affiliation:
Department of Mathematics, University of Connecticut, Storrs, Connecticut 06268
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Abstract

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Let R and S be rings, G and H abelian groups, and RG and SH the goup rings of G and H over R and S respectively. In this note we consider what relations must hold between G and H or between R and S if the group rings RG and SH are isomorphic. For example, it is shown that if R and S are integral domains of characteristic zero, G and H torsion abelian groups such that if G has an element of order p then p is not invertible in R, and RG and SH are isomorphic, then the rings R and 5 are isomorphic and the groups G and H are isomorphic.

Keywords

16A27
Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 32 , Issue 1 , 01 March 1989 , pp. 85 - 89
Copyright
Copyright © Canadian Mathematical Society 1989

References

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